$ ext{If the rate constant for some reaction is } k = 3 imes 10^{-4} ext{ L mol}^{-1} ext{s}^{-1}, ext{ then its order is :}$

Question

$	ext{If the rate constant for some reaction is } k = 3 	imes 10^{-4} 	ext{ L mol}^{-1} 	ext{s}^{-1}, 	ext{ then its order is :}$

Accepted Answer

To determine the order of a reaction based on the units of the rate constant, we need to understand how the units of the rate constant relate to the reaction order. The general form of the rate law for a reaction is:

$$ \text{Rate} = k [A]^n $$

where:
- $ \text{Rate} $ is typically expressed in units of concentration per time (e.g., mol L$^{-1}$ s$^{-1}$),
- $ k $ is the rate constant,
- $[A]$ is the concentration of the reactant,
- $ n $ is the order of the reaction.

The units of the rate constant $ k $ depend on the overall order of the reaction. For a reaction of order $ n $, the units of $ k $ are:

$$ \text{Units of } k = \text{(concentration)}^{1-n} \times \text{time}^{-1} $$

Given that the rate constant $ k = 3 \times 10^{-4} \text{ L mol}^{-1} \text{s}^{-1} $, we can analyze the units:

- The unit $\text{L mol}^{-1}$ indicates that the concentration term is raised to the power of $-1$, which suggests that the reaction order is $ n = 2 $.

Let's break it down:

1. **Zero Order (Option 1):** For a zero-order reaction, the units of $ k $ would be $\text{mol L}^{-1} \text{s}^{-1}$. This does not match the given units.

2. **First Order (Option 2):** For a first-order reaction, the units of $ k $ would be $\text{s}^{-1}$. This also does not match the given units.

3. **Second Order (Option 3):** For a second-order reaction, the units of $ k $ are $\text{L mol}^{-1} \text{s}^{-1}$. This matches the given units exactly, confirming that the reaction is second order.

4. **Third Order (Option 4):** For a third-order reaction, the units of $ k $ would be $\text{L}^2 \text{mol}^{-2} \text{s}^{-1}$. This does not match the given units.

Therefore, based on the units of the rate constant, the correct order of the reaction is indeed 2, which corresponds to Option 3. This explanation supports the given correct answer without contradiction.